Download MISSING DEGREES OF A TRIANGLE

MISSING DEGREES OF A TRIANGLE
Angles of a Triangle
Just like regular numbers, angles can be added to obtain a sum. Sometimes we can
determine a missing angle because we know that the sum must be a certain value.
Remember -- the sum of the degree measures of angles in any triangle equals 180 degrees.
Below is a picture of triangle ABC, where angle A = 60 degrees, angle B = 50 degrees and
angle C = 70 degrees.
If we add all three angles in any triangle we get 180 degrees. So, the measure of angle A +
angle B + angle C = 180 degrees. This is true for any triangle in the world of geometry. We
can use this idea to find the measure of angle(s) where the degree measure is missing or not
given.
Sample A
In triangle ABC below, angle A = 40 degrees and angle B = 60 degrees. What is the
measure of angle C?
We know that the sum of the measures of any triangle is 180 degrees. Using the fact that
angle A + angle B + angle C = 180 degrees, we can find the measure of angle C.
angle A = 40
angle B = 60
angle C = we don't know.
To find angle C, we simply plug into the formula above and solve for C.
A + B + C = 180
C = 180 - A - B
C = 180 - 40 - 60
C = 80
To check if 80 degrees is correct, let's add all three angle measures. If we get 180 degrees,
then our answer for angle C is right.
Here we go:
40 + 60 + 80 = 180
180 = 180...It checks!
You don't always have to plug in those values to the equation and solve. Once you're
comfortable with this sort of problem you'll be able to say "okay, 40 + 60 =100, so the other
angle has to be 80!" and it's much quicker.
Sample B
If a triangle is equiangular, what is the degree measure of each of its angles?
Remember, all angles of an equiangular triangle have equal measure. Let x = the degree
measure of each angle. Triangles have three vertices and so we will add x THREE times.
We have this:
x + x + x = 180
3x = 180
x = 60
Makes sense, right? If all the angles are equal, and they add up to 180, then it has to be 60
degrees!